Selling coffee is the mission. Providing a place to hang out -- whether for a few minutes waiting for a friend or for a longer time -- is something that may, for some shops, be a means to advance that mission. But I don't think its the mission, or even a core service. If it was, they'd be selling that directly.
> Doubt and rationalize all you want. It won't change the facts.
The unsubstantiated speculation that the people that are doing not-buying-coffee things that you don't like are worth less to the coffee shop than people (including you) who you feel are being blocked by them in your desire to do not-buying-coffee things that you do like is not in any way established to be part of "the facts".